In order to study the collisions between two particles, we shall come across the centre of mass system or centre of mass frame of reference and laboratory system or laboratory frame of reference. A reference frame is the space and this space is determined by a rigid body, which is known as base. The rigid body is supposed to extend in all directions as far as necessary.

Laboratory system (or frame of reference):

When the origin of the reference system is a point which is rigidly fixed to the laboratory, then this type of reference frame is known as the laboratory system or the laboratory frame of reference. If earth is taken to be an inertial frame then the laboratory frame is also a inertial frame of reference.

Centre of mass system (or frame of reference):

When the origin of the reference system is a point which is fixed rigidly to the centre of mass of a system of particles then this type of reference frame is known as the centre of mass frame of reference. In this case there is no external force on the system of particles.

Since the centre of mass of the system of particles is itself the origin of the frame of reference then the position vector of that centre of mass is \( \vec{R}=0 \). Therefore the velocity of the centre of mass is also \( \vec{V}=\frac{d\vec{R}}{dt}=0 \).

If \( M \) be the total mass of the system, then the linear momentum of the system is also zero, \( \vec{P}=M\vec{V}=0 \).

For this reason this type of reference frame is also known as zero momentum frame.